An analysis of geometric uncertainty calculations for prostate radiotherapy in clinical practice.

Margins are used in radiotherapy to assist in the calculation of planning target volumes. These margins can be determined by analysing the geometric uncertainties inherent to the radiotherapy planning and delivery process. An important part of this process is the study of electronic portal images collected throughout the course of treatment. Set-up uncertainties were determined for prostate radiotherapy treatments at our previous site and the new purpose-built centre, with margins determined using a number of different methods. In addition, the potential effect of reducing the action level from 5 mm to 3 mm for changing a patient set-up, based on off-line bony anatomy-based portal image analysis, was studied. Margins generated using different methodologies were comparable. It was found that set-up errors were reduced following relocation to the new centre. Although a significant increase in the number of corrections to a patient's set-up was predicted if the action level was reduced from 5 mm to 3 mm, minimal reduction in patient set-up uncertainties would be seen as a consequence. Prescriptive geometric uncertainty analysis not only supports calculation and justification of the margins used clinically to generate planning target volumes, but may also best be used to monitor trends in clinical practice or audit changes introduced by new equipment, technology or practice. Simulations on existing data showed that a 3 mm rather than a 5 mm action level during off-line, bony anatomy-based portal imaging would have had a minimal benefit for the patients studied in this work.

Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic

Uncertainties associated with the structural model and measured vibration data may lead to unreliable damage detection. In this paper, we show that geometric and measurement uncertainty cause considerable problem in damage assessment which can be alleviated by using a fuzzy logic-based approach for damage detection. Curvature damage factor (CDF) of a tapered cantilever beam are used as damage indicators. Monte Carlo simulation (MCS) is used to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. Variation in these CDF measures due to randomness in structural parameter, further contaminated with measurement noise, are used for developing and testing a fuzzy logic system (FLS). Results show that the method correctly identifies both single and multiple damages in the structure. For example, the FLS detects damage with an average accuracy of about 95 percent in a beam having geometric uncertainty of 1 percent COV and measurement noise of 10 percent in single damage scenario. For multiple damage case, the FLS identifies damages in the beam with an average accuracy of about 94 percent in the presence of above mentioned uncertainties. The paper brings together the disparate areas of probabilistic analysis and fuzzy logic to address uncertainty in structural damage detection.

Feature Matching for Object Localization in the Presence of Uncertainty

We consider the problem of matching model and sensory data features in the presence of geometric uncertainty, for the purpose of object localization and identification. The problem is to construct sets of model feature and sensory data feature pairs that are geometrically consistent given that there is uncertainty in the geometry of the sensory data features. If there is no geometric uncertainty, polynomial-time algorithms are possible for feature matching, yet these approaches can fail when there is uncertainty in the geometry of data features. Existing matching and recognition techniques which account for the geometric uncertainty in features either cannot guarantee finding a correct solution, or can construct geometrically consistent sets of feature pairs yet have worst case exponential complexity in terms of the number of features. The major new contribution of this work is to demonstrate a polynomial-time algorithm for constructing sets of geometrically consistent feature pairs given uncertainty in the geometry of the data features. We show that under a certain model of geometric uncertainty the feature matching problem in the presence of uncertainty is of polynomial complexity. This has important theoretical implications by demonstrating an upper bound on the complexity of the matching problem, an by offering insight into the nature of the matching problem itself. These insights prove useful in the solution to the matching problem in higher dimensional cases as well, such as matching three-dimensional models to either two or three-dimensional sensory data. The approach is based on an analysis of the space of feasible transformation parameters. This paper outlines the mathematical basis for the method, and describes the implementation of an algorithm for the procedure. Experiments demonstrating the method are reported.

Cellular signalling effects in high precision radiotherapy

Radiotherapy is commonly planned on the basis of physical dose received by the tumour and surrounding normal tissue, with margins added to address the possibility of geometric miss. However, recent experimental evidence suggests that intercellular signalling results in a given cell's survival also depending on the dose received by neighbouring cells. A model of radiation-induced cell killing and signalling was used to analyse how this effect depends on dose and margin choices. Effective Uniform Doses were calculated for model tumours in both idealised cases with no delivery uncertainty and more realistic cases incorporating geometric uncertainty. In highly conformal irradiation, a lack of signalling from outside the target leads to reduced target cell killing, equivalent to under-dosing by up to 10% compared to large uniform fields. This effect is significantly reduced when higher doses per fraction are considered, both increasing the level of cell killing and reducing margin sensitivity. These effects may limit the achievable biological precision of techniques such as stereotactic radiotherapy even in the absence of geometric uncertainties, although it is predicted that larger fraction sizes reduce the relative contribution of cell signalling driven effects. These observations may contribute to understanding the efficacy of hypo-fractionated radiotherapy.

Evaluating deviations in prostatectomy patients treated with IMRT

Aim - To evaluate the deviations in prostatectomy patients treated with IMRT in order to calculate appropriate margins to create the PTV. Background - Defining inappropriate margins can lead to underdosing in target volumes and also overdosing in healthy tissues, increasing morbidity. Material and methods - 223 CBCT images used for alignment with the CT planning scan based on bony anatomy were analyzed in 12 patients treated with IMRT following prostatectomy. Shifts of CBCT images were recorded in three directions to calculate the required margin to create PTV. Results and discussion - The mean and standard deviation (SD) values in millimetres were −0.05 ± 1.35 in the LR direction, −0.03 ± 0.65 in the SI direction and −0.02 ± 2.05 the AP direction. The systematic error measured in the LR, SI and AP direction were 1.35 mm, 0.65 mm, and 2.05 mm with a random error of 2.07 mm; 1.45 mm and 3.16 mm, resulting in a PTV margin of 4.82 mm; 2.64 mm, and 7.33 mm, respectively. Conclusion - With IGRT we suggest a margin of 5 mm, 3 mm and 8 mm in the LR, SI and AP direction, respectively, to PTV1 and PTV2. Therefore, this study supports an anisotropic margin expansion to the PTV being the largest expansion in the AP direction and lower in SI.

Error and uncertainty of adult age estimation of the pubic symphysis in an Australian sub-population using computed tomography

After attending this presentation, attendees will gain awareness of: (1) the error and uncertainty associated with the application of the Suchey-Brooks (S-B) method of age estimation of the pubic symphysis to a contemporary Australian population; (2) the implications of sexual dimorphism and bilateral asymmetry of the pubic symphysis through preliminary geometric morphometric assessment; and (3) the value of three-dimensional (3D) autopsy data acquisition for creating forensic anthropological standards. This presentation will impact the forensic science community by demonstrating that, in the absence of demographically sound skeletal collections, post-mortem autopsy data provides an exciting platform for the construction of large contemporary ‘virtual osteological libraries’ for which forensic anthropological research can be conducted on Australian individuals. More specifically, this study assesses the applicability and accuracy of the S-B method to a contemporary adult population in Queensland, Australia, and using a geometric morphometric approach, provides an insight to the age-related degeneration of the pubic symphysis. Despite the prominent use of the Suchey-Brooks (1990) method of age estimation in forensic anthropological practice, it is subject to intrinsic limitations, with reports of differential inter-population error rates between geographical locations1-4. Australian forensic anthropology is constrained by a paucity of population specific standards due to a lack of repositories of documented skeletons. Consequently, in Australian casework proceedings, standards constructed from predominately American reference samples are applied to establish a biological profile. In the global era of terrorism and natural disasters, more specific population standards are required to improve the efficiency of medico-legal death investigation in Queensland. The sample comprises multi-slice computed tomography (MSCT) scans of the pubic symphysis (slice thickness: 0.5mm, overlap: 0.1mm) on 195 individuals of caucasian ethnicity aged 15-70 years. Volume rendering reconstruction of the symphyseal surface was conducted in Amira® (v.4.1) and quantitative analyses in Rapidform® XOS. The sample was divided into ten-year age sub-sets (eg. 15-24) with a final sub-set of 65-70 years. Error with respect to the method’s assigned means were analysed on the basis of bias (directionality of error), inaccuracy (magnitude of error) and percentage correct classification of left and right symphyseal surfaces. Morphometric variables including surface area, circumference, maximum height and width of the symphyseal surface and micro-architectural assessment of cortical and trabecular bone composition were quantified using novel automated engineering software capabilities. The results of this study demonstrated correct age classification utilizing the mean and standard deviations of each phase of the S-B method of 80.02% and 86.18% in Australian males and females, respectively. Application of the S-B method resulted in positive biases and mean inaccuracies of 7.24 (±6.56) years for individuals less than 55 years of age, compared to negative biases and mean inaccuracies of 5.89 (±3.90) years for individuals greater than 55 years of age. Statistically significant differences between chronological and S-B mean age were demonstrated in 83.33% and 50% of the six age subsets in males and females, respectively. Asymmetry of the pubic symphysis was a frequent phenomenon with 53.33% of the Queensland population exhibiting statistically significant (χ2 - p<0.01) differential phase classification of left and right surfaces of the same individual. Directionality was found in bilateral asymmetry, with the right symphyseal faces being slightly older on average and providing more accurate estimates using the S-B method5. Morphometric analysis verified these findings, with the left surface exhibiting significantly greater circumference and surface area than the right (p<0.05). Morphometric analysis demonstrated an increase in maximum height and width of the surface with age, with most significant changes (p<0.05) occurring between the 25-34 and 55-64 year age subsets. These differences may be attributed to hormonal components linked to menopause in females and a reduction in testosterone in males. Micro-architectural analysis demonstrated degradation of cortical composition with age, with differential bone resorption between the medial, ventral and dorsal surfaces of the pubic symphysis. This study recommends that the S-B method be applied with caution in medico-legal death investigations of unknown skeletal remains in Queensland. Age estimation will always be accompanied by error; therefore this study demonstrates the potential for quantitative morphometric modelling of age related changes of the pubic symphysis as a tool for methodological refinement, providing a rigor and robust assessment to remove the subjectivity associated with current pelvic aging methods.

Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

Error Detection and Recovery for Robot Motion Planning with Uncertainty

Robots must plan and execute tasks in the presence of uncertainty. Uncertainty arises from sensing errors, control errors, and uncertainty in the geometry of the environment. The last, which is called model error, has received little previous attention. We present a framework for computing motion strategies that are guaranteed to succeed in the presence of all three kinds of uncertainty. The motion strategies comprise sensor-based gross motions, compliant motions, and simple pushing motions.

On Motion Planning with Uncertainty

Robots must successfully plan and execute tasks in the presence of uncertainty. Uncertainty arises from errors in modeling, sensing, and control. Planning in the presence of uncertainty constitutes one facet of the general motion planning problem in robotics. This problem is concerned with the automatic synthesis of motion strategies from high level task specification and geometric models of environments. In order to develop successful motion strategies, it is necessary to understand the effect of uncertainty on the geometry of object interactions. Object interactions, both static and dynamic, may be represented in geometrical terms. This thesis investigates geometrical tools for modeling and overcoming uncertainty. The thesis describes an algorithm for computing backprojections o desired task configurations. Task goals and motion states are specified in terms of a moving object's configuration space. Backprojections specify regions in configuration space from which particular motions are guaranteed to accomplish a desired task. The backprojection algorithm considers surfaces in configuration space that facilitate sliding towards the goal, while avoiding surfaces on which motions may prematurely halt. In executing a motion for a backprojection region, a plan executor must be able to recognize that a desired task has been accomplished. Since sensors are subject to uncertainty, recognition of task success is not always possible. The thesis considers the structure of backprojection regions and of task goals that ensures goal recognizability. The thesis also develops a representation of friction in configuration space, in terms of a friction cone analogous to the real space friction cone. The friction cone provides the backprojection algorithm with a geometrical tool for determining points at which motions may halt.

Uncertainty evaluation of an axi-symmetric measurement machine

This paper describes a method of uncertainty evaluation for axi-symmetric measurement machines which is compliant with GUM and PUMA methodologies. Specialized measuring machines for the inspection of axisymmetric components enable the measurement of properties such as roundness (radial runout), axial runout and coning. These machines typically consist of a rotary table and a number of contact measurement probes located on slideways. Sources of uncertainty include the probe calibration process, probe repeatability, probe alignment, geometric errors in the rotary table, the dimensional stability of the structure holding the probes and form errors in the reference hemisphere which is used to calibrate the system. The generic method is described and an evaluation of an industrial machine is described as a worked example. Type A uncertainties were obtained from a repeatability study of the probe calibration process, a repeatability study of the actual measurement process, a system stability test and an elastic deformation test. Type B uncertainties were obtained from calibration certificates and estimates. Expanded uncertainties, at 95% confidence, were then calculated for the measurement of; radial runout (1.2 µm with a plunger probe or 1.7 µm with a lever probe); axial runout (1.2 µm with a plunger probe or 1.5 µm with a lever probe); and coning/swash (0.44 arc seconds with a plunger probe or 0.60 arc seconds with a lever probe).

Effect of Geometric Uncertainties on the Aerodynamic Characteristic of Offshore Wind Turbine Blades

Offshore wind turbines operate in a complex unsteady flow environment which causes unsteady aerodynamic loads. The unsteady flow environment is characterized by a high degree of uncertainty. In addition, geometry variations and material imperfections also cause uncertainties in the design process. Probabilistic design methods consider these uncertainties in order to reach acceptable reliability and safety levels for offshore wind turbines. Variations of the rotor blade geometry influence the aerodynamic loads which also affect the reliability of other wind turbine components. Therefore, the present paper is dealing with geometric uncertainties of the rotor blades. These can arise from manufacturing tolerances and operational wear of the blades. First, the effect of geometry variations of wind turbine airfoils on the lift and drag coefficients are investigated using a Latin hypercube sampling. Then, the resulting effects on the performance and the blade loads of an offshore wind turbine are analyzed. The variations of the airfoil geometry lead to a significant scatter of the lift and drag coefficients which also affects the damage-equivalent flapwise bending moments. In contrast to that, the effects on the power and the annual energy production are almost negligible with regard to the assumptions made.

Asset specificity and behavioural uncertainty as moderators of the sales growth : employment growth relationship in emerging ventures

Sales growth and employment growth are the two most widely used growth indicators for new ventures; yet, sales growth and employment growth are not interchangeable measures of new venture growth. Rather, they are related, but somewhat independent constructs that respond differently to a variety of criteria. Most of the literature treats this as a methodological technicality. However, sales growth with or without accompanying employment growth has very different implications for managers and policy makers. A better understanding of what drives these different growth metrics has the potential to lead to better decision making. To improve that understanding we apply transaction cost economics reasoning to predict when sales growth will be or will not be accompanied by employment growth. Our results indicate that our predictions are borne out consistently in resource-constrained contexts but not in resource-munificent contexts.

Investment decision-making under risk (reliability) and uncertainty for infrastructure asset management

Risks and uncertainties are inevitable in engineering projects and infrastructure investments. Decisions about investment in infrastructure such as for maintenance, rehabilitation and construction works can pose risks, and may generate significant impacts on social, cultural, environmental and other related issues. This report presents the results of a literature review of current practice in identifying, quantifying and managing risks and predicting impacts as part of the planning and assessment process for infrastructure investment proposals. In assessing proposals for investment in infrastructure, it is necessary to consider social, cultural and environmental risks and impacts to the overall community, as well as financial risks to the investor. The report defines and explains the concept of risk and uncertainty, and describes the three main methodology approaches to the analysis of risk and uncertainty in investment planning for infrastructure, viz examining a range of scenarios or options, sensitivity analysis, and a statistical probability approach, listed here in order of increasing merit and complexity. Forecasts of costs, benefits and community impacts of infrastructure are recognised as central aspects of developing and assessing investment proposals. Increasingly complex modelling techniques are being used for investment evaluation. The literature review identified forecasting errors as the major cause of risk. The report contains a summary of the broad nature of decision-making tools used by governments and other organisations in Australia, New Zealand, Europe and North America, and shows their overall approach to risk assessment in assessing public infrastructure proposals. While there are established techniques to quantify financial and economic risks, quantification is far less developed for political, social and environmental risks and impacts. The report contains a summary of the broad nature of decision-making tools used by governments and other organisations in Australia, New Zealand, Europe and North America, and shows their overall approach to risk assessment in assessing public infrastructure proposals. While there are established techniques to quantify financial and economic risks, quantification is far less developed for political, social and environmental risks and impacts. For risks that cannot be readily quantified, assessment techniques commonly include classification or rating systems for likelihood and consequence. The report outlines the system used by the Australian Defence Organisation and in the Australian Standard on risk management. After each risk is identified and quantified or rated, consideration can be given to reducing the risk, and managing any remaining risk as part of the scope of the project. The literature review identified use of risk mapping techniques by a North American chemical company and by the Australian Defence Organisation. This literature review has enabled a risk assessment strategy to be developed, and will underpin an examination of the feasibility of developing a risk assessment capability using a probability approach.

Framework for investment decision-making under risk and uncertainty for infrastructure asset management

A study has been conducted to investigate current practices on decision-making under risk and uncertainty for infrastructure project investments. It was found that many European countries such as the UK, France, Germany including Australia use scenarios for the investigation of the effects of risk and uncertainty of project investments. Different alternative scenarios are mostly considered during the engineering economic cost-benefit analysis stage. For instance, the World Bank requires an analysis of risks in all project appraisals. Risk in economic evaluation needs to be addressed by calculating sensitivity of the rate of return for a number of events. Risks and uncertainties of project developments arise from various sources of errors including data, model and forecasting errors. It was found that the most influential factors affecting risk and uncertainty resulted from forecasting errors. Data errors and model errors have trivial effects. It was argued by many analysts that scenarios do not forecast what will happen but scenarios indicate only what can happen from given alternatives. It was suggested that the probability distributions of end-products of the project appraisal, such as cost-benefit ratios that take forecasting errors into account, are feasible decision tools for economic evaluation. Political, social, environmental as well as economic and other related risk issues have been addressed and included in decision-making frameworks, such as in a multi-criteria decisionmaking framework. But no suggestion has been made on how to incorporate risk into the investment decision-making process.